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| '''Archimedes''' of Syracuse, c. 287 - 212 B.C., ] and |
'''Archimedes''' of Syracuse, c. 287 - 212 B.C., ], ] and ]. | ||
| Archimedes is one of the greatest mathematicians of all time. He became a popular figure as a result of his involvement in the defense of Syracuse against the Roman siege in the ]. He is reputed to have held the Romans at bay single-handedly with war engines of his design; to have been able to move a full-size ship complete with crew and cargo by pulling a single rope; to have discovered the principle of buoyancy while taking a bath, taking to the streets naked calling "eureka" (I found it!); and to have invented the irrigation device known as ]. | |||
| In terms of creativity and insight, he exceeds any other mathematician prior to the European renaissance. In a civilization with an awkward number system and a language in which "a myriad" (literally ten thousand) meant "infinity", he invented a positional number system and used it to write numbers up to 10<sup>64</sup>. He use a heuristic method based on statics to do private calculation that we would classify today as integral calculus, but he relied on rigorous geometric proofs to prove his results. To what extent he actually had a correct version of integral calculus is debatable. He proved that the ratio of a circle's perimeter to its diameter is the same as the ratio of the circle's area to the square of the radius. He did not call this ratio π but he did approximate it as "exceeding 3 in less than 1/7 but more than 10/71". He was the first, and pretty much the only, greek mathematician to introduce mechanical curves (those traced by a moving point) as legitimate objects of study, and used ] to square the circle. He proved that the area enclosed by a parabola and a straight line is 4/3 the area of equal base and heoght. He proved that the area and volume of the sphere are in the same ratio to the area and volume of a circumscribed straight cylinder, a result he was so proud of that he made it his epitaph. | |||
| Archimedes is probably also the first mathematical physicist on record, and the best before Galileo and Newton. He invented the field of statics, enunciated the law of the lever, the law of equilibrium of fluids and the law of buoyancy. He gave the equilibrium positions of sections of paraboloids as a function of their height, base area and density, a feat that would be taxing to a modern physicist, using only greek geometry. | |||
| Draft. Some of the obvious things here include: | Draft. Some of the obvious things here include: | ||
Revision as of 11:01, 1 May 2002
Archimedes of Syracuse, c. 287 - 212 B.C., mathematician, physicist and engineer.
Archimedes is one of the greatest mathematicians of all time. He became a popular figure as a result of his involvement in the defense of Syracuse against the Roman siege in the punic wars. He is reputed to have held the Romans at bay single-handedly with war engines of his design; to have been able to move a full-size ship complete with crew and cargo by pulling a single rope; to have discovered the principle of buoyancy while taking a bath, taking to the streets naked calling "eureka" (I found it!); and to have invented the irrigation device known as Archimedes' screw.
In terms of creativity and insight, he exceeds any other mathematician prior to the European renaissance. In a civilization with an awkward number system and a language in which "a myriad" (literally ten thousand) meant "infinity", he invented a positional number system and used it to write numbers up to 10. He use a heuristic method based on statics to do private calculation that we would classify today as integral calculus, but he relied on rigorous geometric proofs to prove his results. To what extent he actually had a correct version of integral calculus is debatable. He proved that the ratio of a circle's perimeter to its diameter is the same as the ratio of the circle's area to the square of the radius. He did not call this ratio π but he did approximate it as "exceeding 3 in less than 1/7 but more than 10/71". He was the first, and pretty much the only, greek mathematician to introduce mechanical curves (those traced by a moving point) as legitimate objects of study, and used Archimedes' spiral to square the circle. He proved that the area enclosed by a parabola and a straight line is 4/3 the area of equal base and heoght. He proved that the area and volume of the sphere are in the same ratio to the area and volume of a circumscribed straight cylinder, a result he was so proud of that he made it his epitaph.
Archimedes is probably also the first mathematical physicist on record, and the best before Galileo and Newton. He invented the field of statics, enunciated the law of the lever, the law of equilibrium of fluids and the law of buoyancy. He gave the equilibrium positions of sections of paraboloids as a function of their height, base area and density, a feat that would be taxing to a modern physicist, using only greek geometry.
Draft. Some of the obvious things here include:
- The "Eureka" thing
- Archimedes' screw
- The principle of the lever
- The buoyancy principle
- Machines invented for the defense of Syracuse
- Books written (yes, they didn't survive intact, but list them anyway)
- Some info on π, or at least a link to π's page.
External links: